DSAT Problem Solving Strategies 2

Question 1

A student needs to find the value of x in the equation 3(x + 4) = 2x + 17. Which first step is most efficient?

Accepted Answer

Distribute 3 on the left side

Answer

Divide both sides by 3

Answer

Subtract 2x from both sides

Answer

Add 17 to both sides

Question 2

When a problem asks for the 'minimum' value of a quadratic expression that opens upward, where is that value located?

Accepted Answer

At the vertex

Answer

At the y-intercept

Answer

At the x-intercepts

Answer

At the axis of symmetry's y-value, which equals the vertex

Question 3

A ratio problem states that for every 3 apples there are 5 oranges. If there are 24 apples, what strategy finds the number of oranges fastest?

Accepted Answer

Set up a proportion: 3/5 = 24/x

Answer

Multiply 24 by 5

Answer

Subtract 3 from 24, then add 5

Answer

Divide 24 by 5, then multiply by 3

Question 4

On the DSAT, if a question involves a complex multi-step word problem, what is the best first action?

Accepted Answer

Identify and label the unknown quantity

Answer

Immediately write an equation

Answer

Try all four answer choices

Answer

Convert all units to the same system

Question 5

A store marks up items by 30%, then applies a 20% discount. A student wants to find the final price of a $100 item. Which approach is correct?

Accepted Answer

100 × 1.30 × 0.80

Answer

100 × (1.30 − 0.20)

Answer

100 × (0.30 − 0.20)

Answer

100 × 1.10

Question 6

When working with an SAT problem involving absolute value |x − 3| = 7, how many solutions should you expect?

Accepted Answer

Two solutions

Answer

Zero solutions

Answer

Exactly one solution

Answer

Infinitely many solutions

Question 7

A question gives a table of values and asks which linear equation fits. What is the most reliable strategy?

Accepted Answer

Calculate the slope from two table points and check the y-intercept

Answer

Pick the equation with the largest slope

Answer

Plug x = 0 into each answer choice

Answer

Choose the equation whose coefficients look simplest